題目
Say you have an array for which the ith element is the price of a given stock on day i.

Design an algorithm to find the maximum profit. You may complete at most two transactions.

Note:
You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

答案

這個答案很巧妙，竟然用到了2個dp數組，然后答案要從2個dp數組的信息中提取出來，把分治和dp巧妙結合起來，讓我學到很多!

class Solution {
    public int maxProfit(int[] prices) {
        if(prices.length == 0) return 0;
        int[] left = new int[prices.length];
        int[] right = new int[prices.length];
        
        int min = prices[0];
        for(int i = 1; i < prices.length; i++) {
            min = Math.min(min, prices[i]);
            left[i] = Math.max(left[i - 1], prices[i] - min);
        }
        
        int max = prices[prices.length - 1];
        for(int i = prices.length - 2; i >= 0; i--) {
            max = Math.max(max, prices[i]);
            right[i] = Math.max(right[i + 1], max - prices[i]);
        }
        
        max = 0;
        for(int i = 0; i < prices.length; i++) {
            max = Math.max(max, left[i] + right[i]);
        }
        return max;
    }
}